Answer to Question #211513 in Algebra for Moe

Question #211513

Let a(x)=a(x) = x32x4x^3 - 2x - 4


Which of the following is true?

  1. a(x))a(x)) is not a polynomial
  2. The remainder when a(x)a(x) is divided by x+2x + 2 is 0
  3. a(x)a(x) is divisible by x2x - 2
  4. a(1)=3a(-1) = 3
  5. None of the above
1
Expert's answer
2021-07-02T10:53:32-0400

a(x))a(x)) is not a polynomial

false because it is a polynomial.


2:

The remainder when a(x) is divided by x+2 is 0

Check

x32x4x+2\frac{x^3-2x-4}{x+2}

Find the next term of the quotient and the remainder

x2+2x22x4x+2x^2+\frac{-2x^2-2x-4}{x+2}


x32x4x+2\frac{x^3-2x-4}{x+2}

Find the next term of the quotient and the remainder m

x32x4x+2\frac{x^3-2x-4}{x+2}

Find the next term of the quotient and the remainder

x22x+2x4x+2x^2-2x+\frac{2x-4}{x+2}

Find the next term of the quotient and the remainder

x22x+2+8x+2x^2-2x+2+\frac{-8}{x+2}

Simplify the sign in the fraction

x22x+28x+2x^2-2x+2-\frac{8}{x+2}


False because the remainder is -8.


3: 

a(x) is divisible by x-2

Check

Use polynomial division for x

x32x4)x2\frac{x^3-2x-4)}{x-2}

Find the next term of the quotient and the remainder

x2+2x22x4x2x^2+\frac{-2x^2-2x-4}{x-2}

Find the next term of the quotient and the remainder

x2+2x+2x4x2x^2+2x+\frac{2x-4}{x-2}

Find the next term of the quotient and the remainder

x2+2x+2x^2+2x+2


True because a(x) divide by 2 is x2+2x+2x^2+2x+2


4:

a(1)=3checka(1)=(1)32(1)4=1+24=5+2=3Falsea(-1)=3\\check\\a(-1)=(-1)^3-2(-1)-4=-1+2-4=-5+2=-3\\False

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